True or false if the dimensions of a cylinder are doubled then its volume is quadrupled.
2 answers:
Answer: The given statement is FALSE.
Step-by-step explanation: We are given to check whether the following statement is true or false :
"If the dimensions of a cylinder are doubled then its volume is quadrupled."
We know that
the volume of a cylinder with radius r units and height h units is given by
If the dimensions are doubled, then the new dimensions will be
R = 2r and H = 2h.
Therefore, the new volume will be
Thus, the volume of the new cylinder will be 8 times the original one, not quadrupled.
So, the given statement is FALSE.
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Usually one will differentiate the function to find the minimum/maximum point, but in this case differentiating yields:
which contains multiple solution if one tries to solve for x when the differentiated form is 0.
I would, though, venture a guess that the minimum value would be (approaching) 5, since the function would be undefined in the vicinity.
If, however, the function is
Then differentiating and equating to 0 yields:
which gives:
or 
We reject x=5 as it is when it ix the maximum and thus,
, for 
which contains multiple solution if one tries to solve for x when the differentiated form is 0.
I would, though, venture a guess that the minimum value would be (approaching) 5, since the function would be undefined in the vicinity.
If, however, the function is
Then differentiating and equating to 0 yields:
which gives:
We reject x=5 as it is when it ix the maximum and thus,